Do right-handed swordfighters have a natural advantage against left-handed ones?

In The Princess Bride, Inigo Montoya decides to duel Westley left-handed, as it’s the only way he can be satisfied and have a match of decent length, or so he thinks. Inigo thus starts off left-handed, and so does Westley. When Inigo switches to the right hand, he quickly gains the advantage over his adversary, until Westley switches to the right hand as well, and ultimately succeeds in defeating Inigo.

Do right-handed swordsmen have a natural advantage over those who are dueling with their left hand?

deleted, thought I was in Cafe

I think the point is that they’re both right handed. So they start the duel, and Montoya is like “this will be a breeze, I will use my weak hand so it’s a challenge” but finds that his opponent is able to match him with his own left hand. So he switches hands, and with his dominant hand overcomes his opponent - until his opponent reveals that he’s not left handed either, and switching to his own dominant hand he overcomes Montoya again.

Since, by default, left-handed duelists are used to fighting right-handed ones as are other right-handed ones. Being left-handed should be an advantage.
How that works out in real duels is another matter.

Regarding Princess bride, I agree with @Babale - they’re handicapping themselves by using their weaker hand to prolong the fight.

Regarding factual efficacy, @crowmanyclouds is pretty much correct, in that if you’re used to fighting right-handed opponents, a lefty is going to be unusual, while the left hander is already used to fighting righties, so they would have an experience advantage, although the actually efficacy is unknown.

Historically though, one on one fights with no other factors aren’t nearly the thing fiction would make them out to be, and in formation fighting of any sort, you’d almost certainly be trained to fight with the right hand, so that (for example) shield walls and pike blocks were not misshapen.

And that leaves out how historically, lefties were trained (both by how tools were made and expectations) to be right handed in practice. Something even my mother, born in the fifties complained about. Many nations continue to put pressure on lefties to comply with right-handedness for that matter.

Bias against left-handed people - Wikipedia.

I did a little bit of fencing back in college, and that was my impression. There is definitely a different feel to fighting someone the same handedness as you then the opposite.

When I, a lefty, was fencing, I was in high demand so righties could practice. The other lefty and I bemoaned the dearth of opportunities we ever had to face off against another lefty.

I don’t have a factual answer, only an opinion as a non-fencing lefty, but ti seems like a natural left-handed swordfighter would have a key advantage-- the left-handed swordfighter would have a lot of experience fighting rightys, but right-handed swordfighters would have much less experience fighting leftys.

From the book:

And so saying he took the six-fingered sword.
And put it into his left hand.
He had begun all his duels left-handed lately. It was good practice for him, and although he was the only living wizard in the world with his regular hand, his right, still, he was more than worthy with his left. Perhaps thirty men alive were his equal when he used his left. Perhaps as many as fifty; perhaps as few as ten.
The man in black was also left-handed and that warmed Inigo; it made things fairer. His weakness against the other man’s strength. All to the good.

And I imagine the book also explicitly outlines his surprise when his opponent switches hands too?

The movie is pretty clear:

    INIGO
I admit it -- you are better than
I am.

	MAN IN BLACK
Then why are you smiling?

Inches from defeat, Inigo is, in fact, all smiles.

	INIGO
Because I know something you
don't know.

	MAN IN BLACK
And what is that?

	INIGO
I am not left-handed.

And he throws the six-fingered sword into his right hand and
immediately, the tide of battle turns.

					CUT TO:

THE MAN IN BLACK

stunned, doing everything be can to keep Inigo by the Cliff
edge. But no use. Slowly at first, he begins to retreat. Now
faster, Inigo is in control and the Man In Black is desperate.

					CUT TO:

INIGO

and the six-fingered sword is all but invisible now, as he
increases his attack, then suddenly switches styles again.

					CUT TO:
						  33.

A ROCKY STAIRCASE leading to a turret-shaped plateau, and
the Man In Black is retreating like mad up the steps and he
can’t stop Inigo – nothing can stop Inigo – and in a
frenzy, the Man In Black makes every feint, tries every
thrust, lets go with all he has left. But he fails.
Everything fails. He tries one or two final desperate moves
but they are nothing.

	MAN IN BLACK
You're amazing!

	INIGO
I ought to be after twenty years.

And now the Man In Black is smashed into a stone pillar,
pinned there under the six fingered sword.

	MAN IN BLACK
	(hollering it out)
There's something I ought to tell
you.

	INIGO
Tell me.

	MAN IN BLACK
I am not left-handed either.

I took a semester of fencing in college, as well; one of my friends was in the class with me, and he was a left-hander (the only one in our class). The coach did, indeed, mention that, at least at first, the lefty would have a bit of an advantage against the rest of us, because it would be a different feel to spar against him, versus anyone else in the class.

Here are the passages from the book.

A left-handed black-masked terror. “You are most excellent,” he said. His rear foot was at the cliff edge. He could retreat no more.
“Thank you,” the man in black replied. “I have worked very hard to become so.”
“You are better than I am,” Inigo admitted.
“So it seems. But if that is true, then why are you smiling?”
“Because,” Inigo answered. “I know something you don’t know.”
“And what is that?” asked the man in black.
“I’m not left-handed,” Inigo replied, and with those words he all but threw the six-fingered sword into his right hand, and the tide of battle turned.

And later:

“You can not tell it,” he said then, “because I wear a cape and a mask. But I am smiling now.”
“Why?”
“Because I’m not left-handed either,” said the man in black.
And he too switched hands. And the battle was finally joined.
And Inigo began to retreat.
Who are you?” he screamed.
“No one of import. Another lover of the blade.”
“I must know!”
“Get used to disappointment.”

I did a bit of fencing - and much more other martial arts, including knife and stick. There is no advantage against a righty or lefty - just what you are used to, both in terms of offense and defense. An experienced fencer should have no difficulty. Same as a right-handed boxer should have no difficulty fighting a lefty.

I never encountered a fencer who practiced and competed both left and right-handed. Think of an analogy to baseball or golf. Sure, there are occasional switch hitters, and pro golfers can hit an occasional shot from the other side. But in nearly every situation, if a righty told a pitcher he would bat lefty, he would be indicating that he was going himself a handicap.

In most martial arts other than fencing, the common practice was to work from both leads, and against both leads, so you could respond to any threat no matter where it came from. Wouldn’t have to say, “Wait a minute while I adjust my stance.”

Nearly every fighter has different strengths and weaknesses from various stances, and at times, may switch stances. My main school followed JKD, which stresses a strong right lead/jab. Which is opposite to how most right handed boxers stand. And the standard progression was to work hardest on whatever technique was the weakest from whichever side. I had a really strong/quick right lead punch. So I put far more work into improving my LEFT lead punch.

But fighting right or left against a righty or lefty? Not an issue. Just opens up different lines.